# Authors: The MNE-Python contributors.
# License: BSD-3-Clause
# Copyright the MNE-Python contributors.

from contextlib import nullcontext
from copy import deepcopy
from inspect import signature

import numpy as np
import pytest
from numpy.testing import (
    assert_allclose,
    assert_array_almost_equal,
    assert_array_equal,
    assert_array_less,
)
from scipy import linalg
from scipy.spatial.distance import cdist

import mne
from mne import (
    EvokedArray,
    VolSourceEstimate,
    VolVectorSourceEstimate,
    compute_rank,
    convert_forward_solution,
    pick_channels_cov,
    read_forward_solution,
    read_vectorview_selection,
)
from mne._fiff.compensator import set_current_comp
from mne._fiff.constants import FIFF
from mne.beamformer import (
    Beamformer,
    apply_lcmv,
    apply_lcmv_cov,
    apply_lcmv_epochs,
    apply_lcmv_raw,
    make_dics,
    make_lcmv,
    read_beamformer,
)
from mne.beamformer._compute_beamformer import _prepare_beamformer_input
from mne.datasets import testing
from mne.minimum_norm import apply_inverse, make_inverse_operator
from mne.minimum_norm.tests.test_inverse import _assert_free_ori_match
from mne.simulation import simulate_evoked
from mne.transforms import apply_trans, invert_transform
from mne.utils import _record_warnings, catch_logging, object_diff

data_path = testing.data_path(download=False)
fname_raw = data_path / "MEG" / "sample" / "sample_audvis_trunc_raw.fif"
fname_cov = data_path / "MEG" / "sample" / "sample_audvis_trunc-cov.fif"
fname_fwd = data_path / "MEG" / "sample" / "sample_audvis_trunc-meg-eeg-oct-4-fwd.fif"
fname_fwd_vol = data_path / "MEG" / "sample" / "sample_audvis_trunc-meg-vol-7-fwd.fif"
fname_event = data_path / "MEG" / "sample" / "sample_audvis_trunc_raw-eve.fif"
fname_label = data_path / "MEG" / "sample" / "labels" / "Aud-lh.label"
ctf_fname = data_path / "CTF" / "somMDYO-18av.ds"

reject = dict(grad=4000e-13, mag=4e-12)


def _read_forward_solution_meg(*args, **kwargs):
    fwd = read_forward_solution(*args)
    fwd = convert_forward_solution(fwd, **kwargs)
    return mne.pick_types_forward(fwd, meg=True, eeg=False)


def _get_data(
    tmin=-0.1,
    tmax=0.15,
    all_forward=True,
    epochs=True,
    epochs_preload=True,
    data_cov=True,
    proj=True,
):
    """Read in data used in tests."""
    label = mne.read_label(fname_label)
    events = mne.read_events(fname_event)
    raw = mne.io.read_raw_fif(fname_raw, preload=True)
    forward = mne.read_forward_solution(fname_fwd)
    if all_forward:
        forward_surf_ori = _read_forward_solution_meg(fname_fwd, surf_ori=True)
        forward_fixed = _read_forward_solution_meg(
            fname_fwd, force_fixed=True, surf_ori=True, use_cps=False
        )
        forward_vol = _read_forward_solution_meg(fname_fwd_vol)
    else:
        forward_surf_ori = None
        forward_fixed = None
        forward_vol = None

    event_id, tmin, tmax = 1, tmin, tmax

    # Setup for reading the raw data
    raw.info["bads"] = ["MEG 2443", "EEG 053"]  # 2 bad channels
    # Set up pick list: MEG - bad channels
    left_temporal_channels = read_vectorview_selection("Left-temporal")
    picks = mne.pick_types(raw.info, meg=True, selection=left_temporal_channels)
    picks = picks[::2]  # decimate for speed
    # add a couple channels we will consider bad
    bad_picks = [100, 101]
    bads = [raw.ch_names[pick] for pick in bad_picks]
    assert not any(pick in picks for pick in bad_picks)
    picks = np.concatenate([picks, bad_picks])
    raw.pick([raw.ch_names[ii] for ii in picks])
    del picks

    raw.info["bads"] = bads  # add more bads
    if proj:
        raw.info.normalize_proj()  # avoid projection warnings
    else:
        raw.del_proj()

    if epochs:
        # Read epochs
        epochs = mne.Epochs(
            raw,
            events,
            event_id,
            tmin,
            tmax,
            proj=True,
            baseline=(None, 0),
            preload=epochs_preload,
            reject=reject,
        )
        if epochs_preload:
            epochs.resample(200, npad=0)
        epochs.crop(0, None)
        evoked = epochs.average()
        info = evoked.info
    else:
        epochs = None
        evoked = None
        info = raw.info

    noise_cov = mne.read_cov(fname_cov)
    noise_cov["projs"] = []  # avoid warning
    noise_cov = mne.cov.regularize(
        noise_cov, info, mag=0.05, grad=0.05, eeg=0.1, proj=True, rank=None
    )
    if data_cov:
        data_cov = mne.compute_covariance(
            epochs, tmin=0.04, tmax=0.145, verbose="error"
        )  # baseline warning
    else:
        data_cov = None

    return (
        raw,
        epochs,
        evoked,
        data_cov,
        noise_cov,
        label,
        forward,
        forward_surf_ori,
        forward_fixed,
        forward_vol,
    )


@pytest.mark.slowtest
@testing.requires_testing_data
def test_lcmv_vector():
    """Test vector LCMV solutions."""
    info = mne.io.read_raw_fif(fname_raw).info

    # For speed and for rank-deficiency calculation simplicity,
    # just use grads
    info = mne.pick_info(info, mne.pick_types(info, meg="grad", exclude=()))
    with info._unlock():
        info.update(bads=[], projs=[])

    forward = mne.read_forward_solution(fname_fwd)
    forward = mne.pick_channels_forward(forward, info["ch_names"])
    vertices = [s["vertno"][::200] for s in forward["src"]]
    n_vertices = sum(len(v) for v in vertices)
    assert n_vertices == 4

    amplitude = 100e-9
    stc = mne.SourceEstimate(
        amplitude * np.eye(n_vertices), vertices, 0, 1.0 / info["sfreq"]
    )
    forward_sim = mne.convert_forward_solution(
        forward, force_fixed=True, use_cps=True, copy=True
    )
    forward_sim = mne.forward.restrict_forward_to_stc(forward_sim, stc)
    noise_cov = mne.make_ad_hoc_cov(info)
    noise_cov.update(data=np.diag(noise_cov["data"]), diag=False)
    evoked = simulate_evoked(forward_sim, stc, info, noise_cov, nave=1)
    source_nn = forward_sim["source_nn"]
    source_rr = forward_sim["source_rr"]

    # Figure out our indices
    mask = np.concatenate(
        [np.isin(s["vertno"], v) for s, v in zip(forward["src"], vertices)]
    )
    mapping = np.where(mask)[0]
    assert_array_equal(source_rr, forward["source_rr"][mapping])

    # Don't check NN because we didn't rotate to surf ori
    del forward_sim

    # Let's do minimum norm as a sanity check (dipole_fit is slower)
    inv = make_inverse_operator(info, forward, noise_cov, loose=1.0)
    stc_vector_mne = apply_inverse(evoked, inv, pick_ori="vector")
    mne_ori = stc_vector_mne.data[mapping, :, np.arange(n_vertices)]
    mne_ori /= np.linalg.norm(mne_ori, axis=-1)[:, np.newaxis]
    mne_angles = np.rad2deg(np.arccos(np.sum(mne_ori * source_nn, axis=-1)))
    assert np.mean(mne_angles) < 36

    # Now let's do LCMV
    data_cov = mne.make_ad_hoc_cov(info)  # just a stub for later
    with pytest.raises(ValueError, match="pick_ori"):
        make_lcmv(info, forward, data_cov, 0.05, noise_cov, pick_ori="bad")

    lcmv_ori = list()
    for ti in range(n_vertices):
        this_evoked = evoked.copy().crop(evoked.times[ti], evoked.times[ti])
        data_cov["diag"] = False
        data_cov["data"] = (
            np.outer(this_evoked.data, this_evoked.data) + noise_cov["data"]
        )
        vals = linalg.svdvals(data_cov["data"])
        assert vals[0] / vals[-1] < 1e5  # not rank deficient

        with catch_logging() as log:
            filters = make_lcmv(info, forward, data_cov, 0.05, noise_cov, verbose=True)
        log = log.getvalue()
        assert "498 sources" in log
        with catch_logging() as log:
            filters_vector = make_lcmv(
                info,
                forward,
                data_cov,
                0.05,
                noise_cov,
                pick_ori="vector",
                verbose=True,
            )
        log = log.getvalue()
        assert "498 sources" in log
        stc = apply_lcmv(this_evoked, filters)
        stc_vector = apply_lcmv(this_evoked, filters_vector)
        assert isinstance(stc, mne.SourceEstimate)
        assert isinstance(stc_vector, mne.VectorSourceEstimate)
        assert_allclose(stc.data, stc_vector.magnitude().data)

        # Check the orientation by pooling across some neighbors, as LCMV can
        # have some "holes" at the points of interest
        idx = np.where(cdist(forward["source_rr"], source_rr[[ti]]) < 0.02)[0]
        lcmv_ori.append(np.mean(stc_vector.data[idx, :, 0], axis=0))
        lcmv_ori[-1] /= np.linalg.norm(lcmv_ori[-1])

    lcmv_angles = np.rad2deg(np.arccos(np.sum(lcmv_ori * source_nn, axis=-1)))
    assert np.mean(lcmv_angles) < 55


@pytest.mark.slowtest
@testing.requires_testing_data
@pytest.mark.parametrize(
    "reg, proj, kind",
    [
        (0.01, True, "volume"),
        (0.0, False, "volume"),
        (0.01, False, "surface"),
        (0.0, True, "surface"),
    ],
)
def test_make_lcmv_bem(tmp_path, reg, proj, kind):
    """Test LCMV with evoked data and single trials."""
    pytest.importorskip("h5io")
    (
        raw,
        epochs,
        evoked,
        data_cov,
        noise_cov,
        label,
        forward,
        forward_surf_ori,
        forward_fixed,
        forward_vol,
    ) = _get_data(proj=proj)

    if kind == "surface":
        fwd = forward
    else:
        fwd = forward_vol
        assert kind == "volume"

    filters = make_lcmv(evoked.info, fwd, data_cov, reg=reg, noise_cov=noise_cov)
    stc = apply_lcmv(evoked, filters)
    stc.crop(0.02, None)

    # Smoke test for label= support for surfaces only
    label = mne.read_label(fname_label)
    if kind == "volume":
        ctx = pytest.raises(ValueError, match="volume source space")
    else:
        ctx = nullcontext()
    with ctx:
        make_lcmv(evoked.info, fwd, data_cov, reg=reg, noise_cov=noise_cov, label=label)

    stc_pow = np.sum(np.abs(stc.data), axis=1)
    idx = np.argmax(stc_pow)
    max_stc = stc.data[idx]
    tmax = stc.times[np.argmax(max_stc)]

    assert 0.08 < tmax < 0.15, tmax
    assert 0.9 < np.max(max_stc) < 3.5, np.max(max_stc)

    if kind == "surface":
        # Test picking normal orientation (surface source space only).
        filters = make_lcmv(
            evoked.info,
            forward_surf_ori,
            data_cov,
            reg=reg,
            noise_cov=noise_cov,
            pick_ori="normal",
            weight_norm=None,
        )
        stc_normal = apply_lcmv(evoked, filters)
        stc_normal.crop(0.02, None)

        stc_pow = np.sum(np.abs(stc_normal.data), axis=1)
        idx = np.argmax(stc_pow)
        max_stc = stc_normal.data[idx]
        tmax = stc_normal.times[np.argmax(max_stc)]

        lower = 0.04 if proj else 0.025
        assert lower < tmax < 0.14, tmax
        lower = 3e-7 if proj else 2e-7
        assert lower < np.max(max_stc) < 3e-6, np.max(max_stc)

        # No weight normalization was applied, so the amplitude of normal
        # orientation results should always be smaller than free
        # orientation results.
        assert (np.abs(stc_normal.data) <= stc.data).all()

    # Test picking source orientation maximizing output source power
    filters = make_lcmv(
        evoked.info, fwd, data_cov, reg=reg, noise_cov=noise_cov, pick_ori="max-power"
    )
    stc_max_power = apply_lcmv(evoked, filters)
    stc_max_power.crop(0.02, None)
    stc_pow = np.sum(np.abs(stc_max_power.data), axis=1)
    idx = np.argmax(stc_pow)
    max_stc = np.abs(stc_max_power.data[idx])
    tmax = stc.times[np.argmax(max_stc)]

    lower = 0.08 if proj else 0.04
    assert lower < tmax < 0.15, tmax
    assert 0.8 < np.max(max_stc) < 3.0, np.max(max_stc)

    stc_max_power.data[:, :] = np.abs(stc_max_power.data)

    if kind == "surface":
        # Maximum output source power orientation results should be
        # similar to free orientation results in areas with channel
        # coverage
        label = mne.read_label(fname_label)
        mean_stc = stc.extract_label_time_course(label, fwd["src"], mode="mean")
        mean_stc_max_pow = stc_max_power.extract_label_time_course(
            label, fwd["src"], mode="mean"
        )
        assert_array_less(np.abs(mean_stc - mean_stc_max_pow), 1.0)

    # Test if spatial filter contains src_type
    assert filters["src_type"] == kind

    # __repr__
    assert len(evoked.ch_names) == 22
    assert len(evoked.info["projs"]) == (3 if proj else 0)
    assert len(evoked.info["bads"]) == 2
    rank = 17 if proj else 20
    assert "LCMV" in repr(filters)
    assert "unknown subject" not in repr(filters)
    assert f"{fwd['nsource']} vert" in repr(filters)
    assert "20 ch" in repr(filters)
    assert f"rank {rank}" in repr(filters)

    # I/O
    fname = tmp_path / "filters.h5"
    with pytest.warns(RuntimeWarning, match="-lcmv.h5"):
        filters.save(fname)
    filters_read = read_beamformer(fname)
    assert isinstance(filters, Beamformer)
    assert isinstance(filters_read, Beamformer)
    # deal with object_diff strictness
    filters_read["rank"] = int(filters_read["rank"])
    filters["rank"] = int(filters["rank"])
    assert object_diff(filters, filters_read) == ""

    if kind != "surface":
        return

    # Test if fixed forward operator is detected when picking normal or
    # max-power orientation
    pytest.raises(
        ValueError,
        make_lcmv,
        evoked.info,
        forward_fixed,
        data_cov,
        reg=0.01,
        noise_cov=noise_cov,
        pick_ori="normal",
    )
    pytest.raises(
        ValueError,
        make_lcmv,
        evoked.info,
        forward_fixed,
        data_cov,
        reg=0.01,
        noise_cov=noise_cov,
        pick_ori="max-power",
    )

    # Test if non-surface oriented forward operator is detected when picking
    # normal orientation
    pytest.raises(
        ValueError,
        make_lcmv,
        evoked.info,
        forward,
        data_cov,
        reg=0.01,
        noise_cov=noise_cov,
        pick_ori="normal",
    )

    # Test if volume forward operator is detected when picking normal
    # orientation
    pytest.raises(
        ValueError,
        make_lcmv,
        evoked.info,
        forward_vol,
        data_cov,
        reg=0.01,
        noise_cov=noise_cov,
        pick_ori="normal",
    )

    # Test if missing of noise covariance matrix is detected when more than
    # one channel type is present in the data
    pytest.raises(
        ValueError,
        make_lcmv,
        evoked.info,
        forward_vol,
        data_cov=data_cov,
        reg=0.01,
        noise_cov=None,
        pick_ori="max-power",
    )

    # Test if wrong channel selection is detected in application of filter
    evoked_ch = deepcopy(evoked)
    evoked_ch.pick(evoked_ch.ch_names[1:])
    filters = make_lcmv(
        evoked.info, forward_vol, data_cov, reg=0.01, noise_cov=noise_cov
    )

    # Test if discrepancies in channel selection of data and fwd model are
    # handled correctly in apply_lcmv
    # make filter with data where first channel was removed
    filters = make_lcmv(
        evoked_ch.info, forward_vol, data_cov, reg=0.01, noise_cov=noise_cov
    )
    # applying that filter to the full data set should automatically exclude
    # this channel from the data
    # also test here that no warnings are thrown - implemented to check whether
    # src should not be None warning occurs
    stc = apply_lcmv(evoked, filters)

    # the result should be equal to applying this filter to a dataset without
    # this channel:
    stc_ch = apply_lcmv(evoked_ch, filters)
    assert_array_almost_equal(stc.data, stc_ch.data)

    # Test if non-matching SSP projection is detected in application of filter
    if proj:
        raw_proj = raw.copy().del_proj()
        with pytest.raises(ValueError, match="do not match the projections"):
            apply_lcmv_raw(raw_proj, filters)

    # Test apply_lcmv_raw
    use_raw = raw.copy().crop(0, 1)
    stc = apply_lcmv_raw(use_raw, filters)
    assert_allclose(stc.times, use_raw.times)
    assert_array_equal(stc.vertices[0], forward_vol["src"][0]["vertno"])

    # Test if spatial filter contains src_type
    assert "src_type" in filters

    # check whether a filters object without src_type throws expected warning
    del filters["src_type"]  # emulate 0.16 behaviour to cause warning
    with pytest.warns(RuntimeWarning, match="spatial filter does not contain src_type"):
        apply_lcmv(evoked, filters)

    # Now test single trial using fixed orientation forward solution
    # so we can compare it to the evoked solution
    filters = make_lcmv(
        epochs.info, forward_fixed, data_cov, reg=0.01, noise_cov=noise_cov
    )
    stcs = apply_lcmv_epochs(epochs, filters)
    stcs_ = apply_lcmv_epochs(epochs, filters, return_generator=True)
    assert_array_equal(stcs[0].data, next(stcs_).data)

    epochs.drop_bad()
    assert len(epochs.events) == len(stcs)

    # average the single trial estimates
    stc_avg = np.zeros_like(stcs[0].data)
    for this_stc in stcs:
        stc_avg += this_stc.data
    stc_avg /= len(stcs)

    # compare it to the solution using evoked with fixed orientation
    filters = make_lcmv(
        evoked.info, forward_fixed, data_cov, reg=0.01, noise_cov=noise_cov
    )
    stc_fixed = apply_lcmv(evoked, filters)
    assert_array_almost_equal(stc_avg, stc_fixed.data)

    # use a label so we have few source vertices and delayed computation is
    # not used
    filters = make_lcmv(
        epochs.info, forward_fixed, data_cov, reg=0.01, noise_cov=noise_cov, label=label
    )
    stcs_label = apply_lcmv_epochs(epochs, filters)

    assert_array_almost_equal(stcs_label[0].data, stcs[0].in_label(label).data)

    # Test condition where the filters weights are zero. There should not be
    # any divide-by-zero errors
    zero_cov = data_cov.copy()
    zero_cov["data"][:] = 0
    filters = make_lcmv(
        epochs.info, forward_fixed, zero_cov, reg=0.01, noise_cov=noise_cov
    )
    assert_array_equal(filters["weights"], 0)

    # Test condition where one channel type is picked
    # (avoid "grad data rank (13) did not match the noise rank (None)")
    data_cov_grad = pick_channels_cov(
        data_cov,
        [
            ch_name
            for ch_name in epochs.info["ch_names"]
            if ch_name.endswith(("2", "3"))
        ],
        ordered=False,
    )
    assert len(data_cov_grad["names"]) > 4
    make_lcmv(epochs.info, forward_fixed, data_cov_grad, reg=0.01, noise_cov=noise_cov)


@testing.requires_testing_data
@pytest.mark.slowtest
@pytest.mark.parametrize(
    "weight_norm, pick_ori",
    [
        ("unit-noise-gain", "max-power"),
        ("unit-noise-gain", "vector"),
        ("unit-noise-gain", None),
        ("nai", "vector"),
        (None, "max-power"),
    ],
)
def test_make_lcmv_sphere(pick_ori, weight_norm):
    """Test LCMV with sphere head model."""
    # unit-noise gain beamformer and orientation
    # selection and rank reduction of the leadfield
    _, _, evoked, data_cov, noise_cov, _, _, _, _, _ = _get_data(proj=True)
    assert "eeg" not in evoked
    assert "meg" in evoked
    sphere = mne.make_sphere_model(r0=(0.0, 0.0, 0.0), head_radius=0.080)
    src = mne.setup_volume_source_space(
        pos=25.0, sphere=sphere, mindist=5.0, exclude=2.0
    )
    fwd_sphere = mne.make_forward_solution(evoked.info, None, src, sphere)

    # Test that we get an error if not reducing rank
    with (
        pytest.raises(ValueError, match="Singular matrix detected"),
        _record_warnings(),
        pytest.warns(RuntimeWarning, match="positive semidefinite"),
    ):
        make_lcmv(
            evoked.info,
            fwd_sphere,
            data_cov,
            reg=0.1,
            noise_cov=noise_cov,
            weight_norm=weight_norm,
            pick_ori=pick_ori,
            reduce_rank=False,
            rank="full",
        )

    # Now let's reduce it
    filters = make_lcmv(
        evoked.info,
        fwd_sphere,
        data_cov,
        reg=0.1,
        noise_cov=noise_cov,
        weight_norm=weight_norm,
        pick_ori=pick_ori,
        reduce_rank=True,
    )
    stc_sphere = apply_lcmv(evoked, filters)
    if isinstance(stc_sphere, VolVectorSourceEstimate):
        stc_sphere = stc_sphere.magnitude()
    else:
        stc_sphere = abs(stc_sphere)
    assert isinstance(stc_sphere, VolSourceEstimate)
    stc_sphere.crop(0.02, None)

    stc_pow = np.sum(stc_sphere.data, axis=1)
    idx = np.argmax(stc_pow)
    max_stc = stc_sphere.data[idx]
    tmax = stc_sphere.times[np.argmax(max_stc)]
    assert 0.08 < tmax < 0.15, tmax
    min_, max_ = 1.0, 4.5
    if weight_norm is None:
        min_ *= 2e-7
        max_ *= 2e-7
    assert min_ < np.max(max_stc) < max_, (min_, np.max(max_stc), max_)


@testing.requires_testing_data
@pytest.mark.parametrize("weight_norm", (None, "unit-noise-gain"))
@pytest.mark.parametrize("pick_ori", ("max-power", "normal"))
def test_lcmv_cov(weight_norm, pick_ori):
    """Test LCMV source power computation."""
    (
        raw,
        epochs,
        evoked,
        data_cov,
        noise_cov,
        label,
        forward,
        forward_surf_ori,
        forward_fixed,
        forward_vol,
    ) = _get_data()
    convert_forward_solution(forward, surf_ori=True, copy=False)
    filters = make_lcmv(
        evoked.info,
        forward,
        data_cov,
        noise_cov=noise_cov,
        weight_norm=weight_norm,
        pick_ori=pick_ori,
    )
    for cov in (data_cov, noise_cov):
        this_cov = pick_channels_cov(cov, evoked.ch_names, ordered=False)
        this_evoked = evoked.copy().pick(this_cov["names"])
        this_cov["projs"] = this_evoked.info["projs"]
        assert this_evoked.ch_names == this_cov["names"]
        stc = apply_lcmv_cov(this_cov, filters)
        assert stc.data.min() > 0
        assert stc.shape == (498, 1)
        ev = EvokedArray(this_cov.data, this_evoked.info)
        stc_1 = apply_lcmv(ev, filters)
        assert stc_1.data.min() < 0
        ev = EvokedArray(stc_1.data.T, this_evoked.info)
        stc_2 = apply_lcmv(ev, filters)
        assert stc_2.data.shape == (498, 498)
        data = np.diag(stc_2.data)[:, np.newaxis]
        assert data.min() > 0
        assert_allclose(data, stc.data, rtol=1e-12)


@pytest.mark.slowtest
@testing.requires_testing_data
def test_lcmv_ctf_comp():
    """Test interpolation with compensated CTF data."""
    raw = mne.io.read_raw_ctf(ctf_fname, preload=True)
    raw.pick(raw.ch_names[:70])

    events = mne.make_fixed_length_events(raw, duration=0.2)[:2]
    epochs = mne.Epochs(raw, events, tmin=-0.1, tmax=0.2)
    evoked = epochs.average()

    data_cov = mne.compute_covariance(epochs)
    fwd = mne.make_forward_solution(
        evoked.info,
        None,
        mne.setup_volume_source_space(pos=30.0),
        mne.make_sphere_model(),
    )
    with pytest.raises(ValueError, match="reduce_rank"):
        make_lcmv(evoked.info, fwd, data_cov)
    filters = make_lcmv(evoked.info, fwd, data_cov, reduce_rank=True)
    assert "weights" in filters

    # test whether different compensations throw error
    info_comp = evoked.info.copy()
    set_current_comp(info_comp, 1)
    with pytest.raises(RuntimeError, match="Compensation grade .* not match"):
        make_lcmv(info_comp, fwd, data_cov)


@pytest.mark.slowtest
@testing.requires_testing_data
@pytest.mark.parametrize(
    "proj, weight_norm",
    [
        (True, "unit-noise-gain"),
        (False, "unit-noise-gain"),
        (True, None),
        (True, "nai"),
    ],
)
def test_lcmv_reg_proj(proj, weight_norm):
    """Test LCMV with and without proj."""
    raw = mne.io.read_raw_fif(fname_raw, preload=True)
    events = mne.find_events(raw)
    raw.pick(picks="meg", exclude="bads")
    assert len(raw.ch_names) == 305
    epochs = mne.Epochs(raw, events, None, preload=True, proj=proj)
    with pytest.warns(RuntimeWarning, match="Too few samples"):
        noise_cov = mne.compute_covariance(epochs, tmax=0)
        data_cov = mne.compute_covariance(epochs, tmin=0.04, tmax=0.15)
    forward = mne.read_forward_solution(fname_fwd)
    filters = make_lcmv(
        epochs.info,
        forward,
        data_cov,
        reg=0.05,
        noise_cov=noise_cov,
        pick_ori="max-power",
        weight_norm="nai",
        rank=None,
        verbose=True,
    )
    want_rank = 302  # 305 good channels - 3 MEG projs
    assert filters["rank"] == want_rank
    # And also with and without noise_cov
    with pytest.raises(ValueError, match="several sensor types"):
        make_lcmv(epochs.info, forward, data_cov, reg=0.05, noise_cov=None)
    epochs.pick(picks="grad")
    kwargs = dict(reg=0.05, pick_ori=None, weight_norm=weight_norm)
    filters_cov = make_lcmv(
        epochs.info, forward, data_cov, noise_cov=noise_cov, **kwargs
    )
    filters_nocov = make_lcmv(epochs.info, forward, data_cov, noise_cov=None, **kwargs)
    ad_hoc = mne.make_ad_hoc_cov(epochs.info)
    filters_adhoc = make_lcmv(
        epochs.info, forward, data_cov, noise_cov=ad_hoc, **kwargs
    )
    evoked = epochs.average()
    stc_cov = apply_lcmv(evoked, filters_cov)
    stc_nocov = apply_lcmv(evoked, filters_nocov)
    stc_adhoc = apply_lcmv(evoked, filters_adhoc)

    # Compare adhoc and nocov: scale difference is necessitated by using std=1.
    if weight_norm == "unit-noise-gain":
        scale = np.sqrt(ad_hoc["data"][0])
    else:
        scale = 1.0
    assert_allclose(stc_nocov.data, stc_adhoc.data * scale)
    a = np.dot(filters_nocov["weights"], filters_nocov["whitener"])
    b = np.dot(filters_adhoc["weights"], filters_adhoc["whitener"]) * scale
    atol = np.mean(np.sqrt(a * a)) * 1e-7
    assert_allclose(a, b, atol=atol, rtol=1e-7)

    # Compare adhoc and cov: locs might not be equivalent, but the same
    # general profile should persist, so look at the std and be lenient:
    if weight_norm == "unit-noise-gain":
        adhoc_scale = 0.12
    else:
        adhoc_scale = 1.0
    assert_allclose(
        np.linalg.norm(stc_adhoc.data, axis=0) * adhoc_scale,
        np.linalg.norm(stc_cov.data, axis=0),
        rtol=0.3,
    )
    assert_allclose(
        np.linalg.norm(stc_nocov.data, axis=0) / scale * adhoc_scale,
        np.linalg.norm(stc_cov.data, axis=0),
        rtol=0.3,
    )

    if weight_norm == "nai":
        # NAI is always normalized by noise-level (based on eigenvalues)
        for stc in (stc_nocov, stc_cov):
            assert_allclose(stc.data.std(), 0.584, rtol=0.2)
    elif weight_norm is None:
        # None always represents something not normalized, reflecting channel
        # weights
        for stc in (stc_nocov, stc_cov):
            assert_allclose(stc.data.std(), 2.8e-8, rtol=0.1)
    else:
        assert weight_norm == "unit-noise-gain"
        # Channel scalings depend on presence of noise_cov
        assert_allclose(stc_nocov.data.std(), 7.8e-13, rtol=0.1)
        assert_allclose(stc_cov.data.std(), 0.187, rtol=0.2)


@pytest.mark.slowtest
@pytest.mark.parametrize(
    "reg, weight_norm, use_cov, depth, lower, upper",
    [
        (0.05, "unit-noise-gain", True, None, 97, 98),
        (0.05, "nai", True, None, 96, 98),
        (0.05, "nai", True, 0.8, 96, 98),
        (0.05, None, True, None, 74, 76),
        (0.05, None, True, 0.8, 90, 93),  # depth improves weight_norm=None
        (0.05, "unit-noise-gain", False, None, 83, 86),
        (0.05, "unit-noise-gain", False, 0.8, 83, 86),  # depth same for wn != None
        # no reg
        (0.00, "unit-noise-gain", True, None, 35, 99),  # TODO: Still not stable
    ],
)
def test_localization_bias_fixed(
    bias_params_fixed, reg, weight_norm, use_cov, depth, lower, upper
):
    """Test localization bias for fixed-orientation LCMV."""
    evoked, fwd, noise_cov, data_cov, want = bias_params_fixed
    if not use_cov:
        evoked.pick(picks="grad")
        noise_cov = None
    assert data_cov["data"].shape[0] == len(data_cov["names"])
    loc = apply_lcmv(
        evoked,
        make_lcmv(
            evoked.info,
            fwd,
            data_cov,
            reg,
            noise_cov,
            depth=depth,
            weight_norm=weight_norm,
        ),
    ).data
    loc = np.abs(loc)
    # Compute the percentage of sources for which there is no loc bias:
    perc = (want == np.argmax(loc, axis=0)).mean() * 100
    assert lower <= perc <= upper


# Changes here should be synced with test_dics.py
@pytest.mark.slowtest
@pytest.mark.parametrize(
    "reg, pick_ori, weight_norm, use_cov, depth, lower, upper, lower_ori, upper_ori",
    [
        (
            0.05,
            "vector",
            "unit-noise-gain-invariant",
            False,
            None,
            26,
            28,
            0.82,
            0.84,
        ),  # noqa: E501
        (
            0.05,
            "vector",
            "unit-noise-gain-invariant",
            True,
            None,
            40,
            42,
            0.96,
            0.98,
        ),  # noqa: E501
        (0.05, "vector", "unit-noise-gain", False, None, 13, 14, 0.79, 0.81),
        (0.05, "vector", "unit-noise-gain", True, None, 35, 37, 0.98, 0.99),
        (0.05, "vector", "nai", True, None, 35, 37, 0.98, 0.99),
        (0.05, "vector", None, True, None, 12, 14, 0.97, 0.98),
        (0.05, "vector", None, True, 0.8, 39, 43, 0.97, 0.98),
        (
            0.05,
            "max-power",
            "unit-noise-gain-invariant",
            False,
            None,
            17,
            20,
            0,
            0,
        ),  # noqa: E501
        (0.05, "max-power", "unit-noise-gain", False, None, 17, 20, 0, 0),
        (0.05, "max-power", "nai", True, None, 21, 24, 0, 0),
        (0.05, "max-power", None, True, None, 7, 10, 0, 0),
        (0.05, "max-power", None, True, 0.8, 15, 18, 0, 0),
        (0.05, None, None, True, 0.8, 40, 42, 0, 0),
        # no reg
        (0.00, "vector", None, True, None, 23, 24, 0.96, 0.97),
        (
            0.00,
            "vector",
            "unit-noise-gain-invariant",
            True,
            None,
            52,
            54,
            0.95,
            0.96,
        ),  # noqa: E501
        (0.00, "vector", "unit-noise-gain", True, None, 44, 48, 0.97, 0.99),
        (0.00, "vector", "nai", True, None, 44, 48, 0.97, 0.99),
        (0.00, "max-power", None, True, None, 14, 15, 0, 0),
        (
            0.00,
            "max-power",
            "unit-noise-gain-invariant",
            True,
            None,
            35,
            37,
            0,
            0,
        ),  # noqa: E501
        (0.00, "max-power", "unit-noise-gain", True, None, 35, 37, 0, 0),
        (0.00, "max-power", "nai", True, None, 35, 37, 0, 0),
    ],
)
def test_localization_bias_free(
    bias_params_free,
    reg,
    pick_ori,
    weight_norm,
    use_cov,
    depth,
    lower,
    upper,
    lower_ori,
    upper_ori,
):
    """Test localization bias for free-orientation LCMV."""
    evoked, fwd, noise_cov, data_cov, want = bias_params_free
    if not use_cov:
        evoked.pick(picks="grad")
        noise_cov = None
    with _record_warnings():  # rank deficiency of data_cov
        filters = make_lcmv(
            evoked.info,
            fwd,
            data_cov,
            reg,
            noise_cov,
            pick_ori=pick_ori,
            weight_norm=weight_norm,
            depth=depth,
        )
    loc = apply_lcmv(evoked, filters).data
    if pick_ori == "vector":
        ori = loc.copy() / np.linalg.norm(loc, axis=1, keepdims=True)
    else:
        # doesn't make sense for pooled (None) or max-power (can't be all 3)
        ori = None
    loc = np.linalg.norm(loc, axis=1) if pick_ori == "vector" else np.abs(loc)
    # Compute the percentage of sources for which there is no loc bias:
    max_idx = np.argmax(loc, axis=0)
    perc = (want == max_idx).mean() * 100
    assert lower <= perc <= upper
    _assert_free_ori_match(ori, max_idx, lower_ori, upper_ori)


# Changes here should be synced with the ones above, but these have meaningful
# orientation values
@pytest.mark.parametrize(
    "reg, weight_norm, use_cov, depth, lower, upper, lower_ori, upper_ori",
    [
        (0.05, "unit-noise-gain-invariant", False, None, 38, 40, 0.54, 0.55),
        (0.05, "unit-noise-gain", False, None, 38, 40, 0.54, 0.55),
        (0.05, "nai", True, None, 56, 57, 0.59, 0.61),
        (0.05, None, True, None, 27, 28, 0.56, 0.57),
        (0.05, None, True, 0.8, 42, 43, 0.56, 0.57),
        # no reg
        (0.00, None, True, None, 50, 51, 0.58, 0.59),
        (0.00, "unit-noise-gain-invariant", True, None, 73, 75, 0.59, 0.61),
        (0.00, "unit-noise-gain", True, None, 73, 75, 0.59, 0.61),
        (0.00, "nai", True, None, 73, 75, 0.59, 0.61),
    ],
)
def test_orientation_max_power(
    bias_params_fixed,
    bias_params_free,
    reg,
    weight_norm,
    use_cov,
    depth,
    lower,
    upper,
    lower_ori,
    upper_ori,
):
    """Test orientation selection for bias for max-power LCMV."""
    # we simulate data for the fixed orientation forward and beamform using
    # the free orientation forward, and check the orientation match at the end
    evoked, _, noise_cov, data_cov, want = bias_params_fixed
    fwd = bias_params_free[1]
    if not use_cov:
        evoked.pick(picks="grad")
        noise_cov = None
    filters = make_lcmv(
        evoked.info,
        fwd,
        data_cov,
        reg,
        noise_cov,
        pick_ori="max-power",
        weight_norm=weight_norm,
        depth=depth,
    )
    loc = apply_lcmv(evoked, filters).data
    ori = filters["max_power_ori"]
    assert ori.shape == (246, 3)
    loc = np.abs(loc)
    # Compute the percentage of sources for which there is no loc bias:
    max_idx = np.argmax(loc, axis=0)
    mask = want == max_idx  # ones that localized properly
    perc = mask.mean() * 100
    assert lower <= perc <= upper
    # Compute the dot products of our forward normals and
    assert fwd["coord_frame"] == FIFF.FIFFV_COORD_HEAD
    nn = np.concatenate([s["nn"][v] for s, v in zip(fwd["src"], filters["vertices"])])
    nn = nn[want]
    nn = apply_trans(invert_transform(fwd["mri_head_t"]), nn, move=False)
    assert_allclose(np.linalg.norm(nn, axis=1), 1, atol=1e-6)
    assert_allclose(np.linalg.norm(ori, axis=1), 1, atol=1e-12)
    dots = np.abs((nn[mask] * ori[mask]).sum(-1))
    assert_array_less(dots, 1)
    assert_array_less(0, dots)
    got = np.mean(dots)
    assert lower_ori < got < upper_ori


@pytest.mark.parametrize(
    "weight_norm, pick_ori",
    [
        pytest.param("nai", "max-power", marks=pytest.mark.slowtest),
        pytest.param("unit-noise-gain", "vector", marks=pytest.mark.slowtest),
        ("unit-noise-gain", "max-power"),
        pytest.param("unit-noise-gain", None, marks=pytest.mark.slowtest),
    ],
)
def test_depth_does_not_matter(bias_params_free, weight_norm, pick_ori):
    """Test that depth weighting does not matter for normalized filters."""
    evoked, fwd, noise_cov, data_cov, _ = bias_params_free
    data = apply_lcmv(
        evoked,
        make_lcmv(
            evoked.info,
            fwd,
            data_cov,
            0.05,
            noise_cov,
            pick_ori=pick_ori,
            weight_norm=weight_norm,
            depth=0.0,
        ),
    ).data
    data_depth = apply_lcmv(
        evoked,
        make_lcmv(
            evoked.info,
            fwd,
            data_cov,
            0.05,
            noise_cov,
            pick_ori=pick_ori,
            weight_norm=weight_norm,
            depth=1.0,
        ),
    ).data
    assert data.shape == data_depth.shape
    for d1, d2 in zip(data, data_depth):
        # Sign flips can change when nearly orthogonal to the normal direction
        d2 *= np.sign(np.dot(d1.ravel(), d2.ravel()))
        atol = np.linalg.norm(d1) * 1e-7
        assert_allclose(d1, d2, atol=atol)


@pytest.fixture(scope="session")
def mf_data():
    """Produce Maxwell filtered data for beamforming."""
    raw = mne.io.read_raw_fif(fname_raw).fix_mag_coil_types()
    raw_sss = mne.preprocessing.maxwell_filter(raw)
    events = mne.find_events(raw_sss)
    del raw
    raw_sss.pick(picks="mag")
    assert len(raw_sss.ch_names) == 102
    epochs = mne.Epochs(raw_sss, events)
    data_cov = mne.compute_covariance(epochs, tmin=0)
    fwd = mne.read_forward_solution(fname_fwd)
    return epochs, data_cov, fwd


@testing.requires_testing_data
@pytest.mark.parametrize("use_rank", ("info", "computed", "full", None))
def test_lcmv_maxfiltered(mf_data, use_rank):
    """Test LCMV on maxfiltered data."""
    epochs, data_cov, fwd = mf_data
    rank = compute_rank(data_cov, info=epochs.info)
    assert rank == {"mag": 71}
    ctx = nullcontext()
    if use_rank == "computed":
        use_rank = rank
    elif use_rank is None:
        ctx = pytest.warns(RuntimeWarning, match="rank as it exceeds")
    with catch_logging() as log, ctx:
        make_lcmv(epochs.info, fwd, data_cov, rank=use_rank, verbose=True)
    log = log.getvalue()
    n = 102 if use_rank == "full" else 71
    assert f"Making LCMV beamformer with rank {{'mag': {n}}}" in log


# To reduce test time, only test combinations that should matter rather than
# all of them
@testing.requires_testing_data
@pytest.mark.parametrize(
    "pick_ori, weight_norm, reg, inversion",
    [
        ("vector", "unit-noise-gain-invariant", 0.05, "matrix"),
        ("vector", "unit-noise-gain-invariant", 0.05, "single"),
        ("vector", "unit-noise-gain", 0.05, "matrix"),
        ("vector", "unit-noise-gain", 0.05, "single"),
        ("vector", "unit-noise-gain", 0.0, "matrix"),
        ("vector", "unit-noise-gain", 0.0, "single"),
        ("vector", "nai", 0.05, "matrix"),
        ("max-power", "unit-noise-gain", 0.05, "matrix"),
        ("max-power", "unit-noise-gain", 0.0, "single"),
        ("max-power", "unit-noise-gain", 0.05, "single"),
        ("max-power", "unit-noise-gain-invariant", 0.05, "matrix"),
        ("normal", "unit-noise-gain", 0.05, "matrix"),
        ("normal", "nai", 0.0, "matrix"),
    ],
)
def test_unit_noise_gain_formula(pick_ori, weight_norm, reg, inversion):
    """Test unit-noise-gain filter against formula."""
    raw = mne.io.read_raw_fif(fname_raw, preload=True)
    events = mne.find_events(raw)
    raw.pick(picks="mag")
    assert len(raw.ch_names) == 102
    epochs = mne.Epochs(raw, events, None, preload=True)
    data_cov = mne.compute_covariance(epochs, tmin=0.04, tmax=0.15)
    # for now, avoid whitening to make life easier
    noise_cov = mne.make_ad_hoc_cov(epochs.info, std=dict(grad=1.0, mag=1.0))
    forward = mne.read_forward_solution(fname_fwd)
    convert_forward_solution(forward, surf_ori=True, copy=False)
    rank = None
    kwargs = dict(
        reg=reg,
        noise_cov=noise_cov,
        pick_ori=pick_ori,
        weight_norm=weight_norm,
        rank=rank,
        inversion=inversion,
    )
    if (
        inversion == "single"
        and pick_ori == "vector"
        and weight_norm == "unit-noise-gain-invariant"
    ):
        with pytest.raises(ValueError, match="Cannot use"):
            make_lcmv(epochs.info, forward, data_cov, **kwargs)
        return
    filters = make_lcmv(epochs.info, forward, data_cov, **kwargs)
    _, _, _, _, G, _, _, _ = _prepare_beamformer_input(
        epochs.info,
        forward,
        None,
        "vector",
        noise_cov=noise_cov,
        rank=rank,
        pca=False,
        exp=None,
    )
    n_channels, n_sources = G.shape
    n_sources //= 3
    G.shape = (n_channels, n_sources, 3)
    G = G.transpose(1, 2, 0)  # verts, orient, ch
    _assert_weight_norm(filters, G)


def _assert_weight_norm(filters, G):
    """Check the result of the chosen weight normalization strategy."""
    weights, max_power_ori = filters["weights"], filters["max_power_ori"]

    # Make the dimensions of the weight matrix equal for both DICS (which
    # defines weights for multiple frequencies) and LCMV (which does not).
    if filters["kind"] == "LCMV":
        weights = weights[np.newaxis]
        if max_power_ori is not None:
            max_power_ori = max_power_ori[np.newaxis]
    if max_power_ori is not None:
        max_power_ori = max_power_ori[..., np.newaxis]

    weight_norm = filters["weight_norm"]
    inversion = filters["inversion"]
    n_channels = weights.shape[2]

    if inversion == "matrix":
        # Dipoles are grouped in groups with size n_orient
        n_sources = filters["n_sources"]
        n_orient = 3 if filters["is_free_ori"] else 1
    elif inversion == "single":
        # Every dipole is treated as a unique source
        n_sources = weights.shape[1]
        n_orient = 1

    for wi, w in enumerate(weights):
        w = w.reshape(n_sources, n_orient, n_channels)

        # Compute leadfield in the direction chosen during the computation of
        # the beamformer.
        if filters["pick_ori"] == "max-power":
            use_G = np.sum(G * max_power_ori[wi], axis=1, keepdims=True)
        elif filters["pick_ori"] == "normal":
            use_G = G[:, -1:]
        else:
            use_G = G
        if inversion == "single":
            # Every dipole is treated as a unique source
            use_G = use_G.reshape(n_sources, 1, n_channels)
        assert w.shape == use_G.shape == (n_sources, n_orient, n_channels)

        # Test weight normalization scheme
        got = np.matmul(w, w.conj().swapaxes(-2, -1))
        desired = np.repeat(np.eye(n_orient)[np.newaxis], w.shape[0], axis=0)
        if n_orient == 3 and weight_norm in ("unit-noise-gain", "nai"):
            # only the diagonal is correct!
            assert not np.allclose(got, desired, atol=1e-7)
            got = got.reshape(n_sources, -1)[:, :: n_orient + 1]
            desired = np.ones_like(got)
        if weight_norm == "nai":  # additional scale factor, should be fixed
            atol = 1e-7 * got.flat[0]
            desired *= got.flat[0]
        else:
            atol = 1e-7
        assert_allclose(got, desired, atol=atol, err_msg="w @ w.conj().T = I")

        # Check that the result here is a diagonal matrix for Sekihara
        if n_orient > 1 and weight_norm != "unit-noise-gain-invariant":
            got = w @ use_G.swapaxes(-2, -1)
            diags = np.diagonal(got, 0, -2, -1)
            want = np.apply_along_axis(np.diagflat, 1, diags)
            atol = np.mean(diags).real * 1e-12
            assert_allclose(got, want, atol=atol, err_msg="G.T @ w = θI")


def test_api():
    """Test LCMV/DICS API equivalence."""
    lcmv_names = list(signature(make_lcmv).parameters)
    dics_names = list(signature(make_dics).parameters)
    dics_names[dics_names.index("csd")] = "data_cov"
    dics_names[dics_names.index("noise_csd")] = "noise_cov"
    dics_names.pop(dics_names.index("real_filter"))  # not a thing for LCMV
    assert lcmv_names == dics_names
